Which has the highest freezing point at 1 atm ?

Options

A. 0.1 m NaCl solution
B. 0.1 m ` BaCl_(2)` solution
C. 0.1 m sugar solution
D. 0.1 m `FeCl_(3)` solution

Answer

To determine which solution has the highest freezing point at 1 atm pressure, we can follow these steps:

### Step 1: Understand the Freezing Point Depression Concept
The freezing point depression (ΔTf) is a colligative property that depends on the number of solute particles in a solution. The formula for freezing point depression is given by:

\[ \Delta T_f = i \cdot K_f \cdot m \]

Where:
- \( \Delta T_f \) = depression in freezing point
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( K_f \) = freezing point depression constant of the solvent (for water, it's constant)
- \( m \) = molality of the solution

### Step 2: Identify the Solutions
We have the following solutions to compare:
1. 0.1 M NaCl solution
2. 0.1 M BaCl2 solution
3. 0.1 M Sugar solution
4. 0.1 M FeCl3 solution

### Step 3: Calculate the van 't Hoff Factor (i)
- **For NaCl**: NaCl dissociates into 2 ions (Na⁺ and Cl⁻), so \( i = 2 \).
- **For BaCl2**: BaCl2 dissociates into 3 ions (Ba²⁺ and 2 Cl⁻), so \( i = 3 \).
- **For FeCl3**: FeCl3 dissociates into 4 ions (Fe³⁺ and 3 Cl⁻), so \( i = 4 \).
- **For Sugar**: Sugar does not dissociate in solution, so \( i = 1 \).

### Step 4: Calculate the Depression in Freezing Point for Each Solution
Using the formula for freezing point depression, we can express ΔTf for each solution:

1. **NaCl**:
\[ \Delta T_f = i \cdot K_f \cdot m = 2 \cdot K_f \cdot 0.1 \]

2. **BaCl2**:
\[ \Delta T_f = 3 \cdot K_f \cdot 0.1 \]

3. **FeCl3**:
\[ \Delta T_f = 4 \cdot K_f \cdot 0.1 \]

4. **Sugar**:
\[ \Delta T_f = 1 \cdot K_f \cdot 0.1 \]

### Step 5: Compare the Values of ΔTf
Now we can summarize the values of ΔTf for each solution:
- NaCl: \( 0.2 K_f \)
- BaCl2: \( 0.3 K_f \)
- FeCl3: \( 0.4 K_f \)
- Sugar: \( 0.1 K_f \)

### Step 6: Determine the Highest Freezing Point
The solution with the lowest ΔTf will have the highest freezing point. From our calculations:
- Sugar solution has the lowest ΔTf (0.1 Kf).

### Conclusion
Thus, the solution with the highest freezing point at 1 atm is the **0.1 M Sugar solution**.

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